If 16^x/4^y = 64, which of the following must be true?

Question

If  \frac{16^x}{4^y} = 64 , which of the following must be true?

A. 4x+6=2y
B. 2x−y=6
C. y−2x=3
D. y=2x−3
E. 2y−x=3

0akshay0 · Answer

16^x/4^y = 64 4^{2x}/4^y = 4^3 4^{2x-y} = 4^3 2x-y=3 y=2x-3 Hence Option D is correct. Hit Kudos if you liked it 8-)

HKD1710 · Answer

16 = 2^4
16^x = 2^4x

4 = 2^2
4^y = 2^2y

2^4x / 2^2y = 2^4x-2y

64 = 2^6

2^4x-2y = 2^6

4x-2y = 6
2x-y = 3

y=2x−3 (Choice D)

Abhishek009 · Answer

\frac{16^x}{4^y} = 64

Or,  \frac{2^{4x}}{2^{2y}} = 2^6

Or,  2^{ 4x - 2y } = 2^6

Or,  4x - 2y = 6

Or,  2x - y = 3

Or,  y = 2x - 3

Answer will be (D)  y = 2x - 3

JeffTargetTestPrep · Answer

Let’s simplify each component of the given equation:

16^x = 2^4x

4^y = 2^2y

64 = 2^6

So we have:

(2^4x)/(2^2y) = 2^6

2^(4x - 2y) = 2^6

4x - 2y = 6

4x - 6 = 2y

y = 2x - 3

Answer: D

KSBGC · Answer

it's given ,

16^x / 4^y  =64

( 4^2 )^x  /  4^y  =  4^3

4^{2x} / 4^Y = 4^3
 4^{2x-y}  =  4^3 
2x-y =3
y = 2x -3

Thus the best answer is D.

Ujjwal98 · Answer

I feel the questions should use brackets, i understood that the / is in the power of the digit

Bunuel · Answer

Formatted for better readability.

If 16^x/4^y = 64, which of the following must be true?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If 16^x/4^y = 64, which of the following must be true?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards